Solve {l}{1/2+2/3+3/2}{1/2-frac{2}{3}+frac{5}{3}}

$$\left. \begin{array} { l } { \frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 2 } } \\ { \frac { 1 } { 2 } - \frac { 2 } { 3 } + \frac { 5 } { 3 } } \end{array} \right.$$

Sort

$$\frac{3}{2},\frac{8}{3}$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$sort(\frac{3}{6}+\frac{4}{6}+\frac{3}{2},\frac{1}{2}-\frac{2}{3}+\frac{5}{3})$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$sort(\frac{3+4}{6}+\frac{3}{2},\frac{1}{2}-\frac{2}{3}+\frac{5}{3})$$

Add 3 and 4 to get 7.

$$sort(\frac{7}{6}+\frac{3}{2},\frac{1}{2}-\frac{2}{3}+\frac{5}{3})$$

Least common multiple of 6 and 2 is 6. Convert \frac{7}{6} and \frac{3}{2} to fractions with denominator 6.

$$sort(\frac{7}{6}+\frac{9}{6},\frac{1}{2}-\frac{2}{3}+\frac{5}{3})$$

Since \frac{7}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$sort(\frac{7+9}{6},\frac{1}{2}-\frac{2}{3}+\frac{5}{3})$$

Add 7 and 9 to get 16.

$$sort(\frac{16}{6},\frac{1}{2}-\frac{2}{3}+\frac{5}{3})$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$sort(\frac{8}{3},\frac{1}{2}-\frac{2}{3}+\frac{5}{3})$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$sort(\frac{8}{3},\frac{3}{6}-\frac{4}{6}+\frac{5}{3})$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{8}{3},\frac{3-4}{6}+\frac{5}{3})$$

Subtract 4 from 3 to get -1.

$$sort(\frac{8}{3},-\frac{1}{6}+\frac{5}{3})$$

Least common multiple of 6 and 3 is 6. Convert -\frac{1}{6} and \frac{5}{3} to fractions with denominator 6.

$$sort(\frac{8}{3},-\frac{1}{6}+\frac{10}{6})$$

Since -\frac{1}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$sort(\frac{8}{3},\frac{-1+10}{6})$$

Add -1 and 10 to get 9.

$$sort(\frac{8}{3},\frac{9}{6})$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$sort(\frac{8}{3},\frac{3}{2})$$

Least common denominator of the numbers in the list \frac{8}{3},\frac{3}{2} is 6. Convert numbers in the list to fractions with denominator 6.

$$\frac{16}{6},\frac{9}{6}$$

To sort the list, start from a single element \frac{16}{6}.

$$\frac{16}{6}$$

Insert \frac{9}{6} to the appropriate location in the new list.

$$\frac{9}{6},\frac{16}{6}$$

Replace the obtained fractions with the initial values.

$$\frac{3}{2},\frac{8}{3}$$

Evaluate

$$\frac{8}{3},\ \frac{3}{2}$$